Problem: What is the remainder when the sum of the first 102 counting numbers is divided by 5250?  (The first counting number is 1.)
For all $n$, $1 + 2 + \dots + n = n(n + 1)/2$, so $1 + 2 + \dots + 102 = 102 \cdot 103/2 = 5253$.  The remainder when 5253 is divided by 5250 is $\boxed{3}$.